A multilevel algorithm using Schur-complement factorization on interlevel corrections eliminates polynomial h-dependent readout overhead for observables with χ≤2 in quantum elliptic PDE solvers, achieving near-Heisenberg scaling with amplitude estimation.
Yang and J.-P
7 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
years
2026 7verdicts
UNVERDICTED 7representative citing papers
Develops Weyl-calculus-based LCHS formulas for analytic f(A) yielding O(log 1/ε) quantum eigenvalue transformation and 2.1× cheaper time-dependent ODE simulation.
Presents structure-preserving quantum method-of-lines algorithms for parabolic and hyperbolic PDEs with mixed BCs, using Coons interpolation, similarity transforms, and explicit quantum circuit constructions with complexity and error bounds.
Quantum circuit framework for advection-diffusion PDEs with Robin and periodic boundary conditions via LCHS, including LCU error analysis and gate complexity showing potential quantum advantage in high dimensions.
Quantum-accelerated MLMC methods for BDSDE-based SPDE derivative pricing and Greeks achieve sampling complexity improvement from O(ε^{-2}) to O(ε^{-1}).
Quantum algorithm for 1D NLSE via Lax-pair scattering performs time evolution analytically in the scattering domain and reconstructs solutions with QSVT.
Human-AI collaboration expanded a meta-idea on rational approximation into sign-embedding quantum algorithms for matrix problems, with humans retaining final judgment on routes and refinements.
citing papers explorer
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Toward Efficient End-to-End Quantum Elliptic PDE Solvers: a Multilevel Correction Algorithm for Direct Observable Estimation
A multilevel algorithm using Schur-complement factorization on interlevel corrections eliminates polynomial h-dependent readout overhead for observables with χ≤2 in quantum elliptic PDE solvers, achieving near-Heisenberg scaling with amplitude estimation.
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Quantum Eigenvalue Transformation via Linear Combination of Hamiltonian Simulation: A Weyl Calculus Approach
Develops Weyl-calculus-based LCHS formulas for analytic f(A) yielding O(log 1/ε) quantum eigenvalue transformation and 2.1× cheaper time-dependent ODE simulation.
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Structure-Preserving Quantum Method of Lines for Evolutionary PDEs with Mixed Boundary Conditions
Presents structure-preserving quantum method-of-lines algorithms for parabolic and hyperbolic PDEs with mixed BCs, using Coons interpolation, similarity transforms, and explicit quantum circuit constructions with complexity and error bounds.
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Quantum circuits for the advection-diffusion equation with boundary conditions based on LCHS
Quantum circuit framework for advection-diffusion PDEs with Robin and periodic boundary conditions via LCHS, including LCU error analysis and gate complexity showing potential quantum advantage in high dimensions.
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Quantum Derivative Pricing for SPDEs via BDSDE Representation
Quantum-accelerated MLMC methods for BDSDE-based SPDE derivative pricing and Greeks achieve sampling complexity improvement from O(ε^{-2}) to O(ε^{-1}).
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Quantum algorithm for the nonlinear Schr\"odinger equation via the Lax-pair scattering
Quantum algorithm for 1D NLSE via Lax-pair scattering performs time evolution analytically in the scattering domain and reconstructs solutions with QSVT.
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From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms
Human-AI collaboration expanded a meta-idea on rational approximation into sign-embedding quantum algorithms for matrix problems, with humans retaining final judgment on routes and refinements.